$1.$ If a refinery processes $100,000$ barrels of crude oil per day and yields $50\%$ gasoline, how many barrels of gasoline are produced daily?

$2.$ A catalytic cracking unit processes $20,000$ barrels of heavy oil per day and produces $60\%$ gasoline. How many barrels of gasoline are produced daily?

$3.$ In a hydrocracking process, $10,000$ barrels of heavy oil are converted into lighter products with a yield of $80\%.$ How many barrels of lighter products are obtained?

$4.$ If a reforming unit processes $15,000$ barrels of naphtha and produces $70\%$ high$-$octane gasoline, how many barrels of high$-$octane gasoline are produced?